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WASHINGTON — A private measure of the U.S. services sector contracted for the seventh straight month in April but at a slower pace, the latest sign the economic downturn could be moderating.

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The services index from the Institute for Supply Management, a Tempe, Ariz.-based trade group of purchasing executives, came in at 43.7 in April compared with 40.8 in March. Any reading below 50 indicates the service sector, where most Americans work, is contracting.

Still, Tuesday’s reading was higher than economists expected and provided another sign the economy’s steep downturn could be bottoming out.

The services index is based on a survey of the institute’s members in 18 industries and covers such indicators as new orders, employment and inventories.

New orders surged last month, rising to 47, from 38.8 in March. Economists were encouraged by the jump and said it could be a sign of better days ahead since increased demand is a signal that production will need to rise in coming months.

“The services sector is beginning to show signs that the worst may be behind it,” said Joel Naroff, chief economist at Naroff Economic Advisors.

About three-quarters of Americans work in service-providing industries such as hotels, retail, education and health care. The index showed that seven industries reported growth in April while 11 contracted.

The employment category of the index also showed a gain, rising to 37 from 32.3 in March. But that reading is stuck far below the 50 seen as a break-even point.

Economists believe the national unemployment report, scheduled for release Friday, will show a net total of 620,000 jobs lost in April, slightly below March’s tally of 663,000. They expect the jobless rate, which hit a 25-year high of 8.5 percent in March, rose to 8.9 percent last month.

Federal Reserve Chairman Ben Bernanke told Congress Tuesday that the economy should pull out of a recession and start growing again later this year, but he cautioned that the unemployment rate could remain high for some time.

Retailers have not been immune from the job cuts. Outdoors outfitter L.L. Bean Inc. notified employees last month that it planned to lay off 200 to 240 workers in Maine because of lagging sales.

The overall economy, as measured by the gross domestic product, contracted at an annual rate of 6.1 percent in the first three months of this year after shrinking 6.3 percent in the final quarter of 2008. That marked the worst six-month performance in a half-century.

Many economists are forecasting that the GDP will drop at annual rate of between 1 and 3 percent in the current quarter.